TITLE: Prove that $16 ^ {2023} + 1$ is divisible by $17 ^ 2$.
QUESTION [10 upvotes]: Prove that $16 ^ {2023} + 1$ is divisible by $17 ^ 2$.

It is clear that $16 ^ {2023} + 1$ is divisible by $17$, but why it is divisible by $17 ^ 2$ is not clear.

REPLY [6 votes]: The hint.
Use $2023=7\cdot17^2$, $16=17-1$  and the binomial of Newton.
Now we see that $16^{2023}+1$ is divisible even by $17^3$.